'Loop' of clues with 45 cell 'hole'.

- Code: Select all
`+-------+-------+-------+`

| . 6 3 | 5 7 . | 4 2 . |

| 5 . . | . . 3 | . . 7 |

| 1 . . | . . . | . . 9 |

+-------+-------+-------+

| . 5 . | . . . | . . 4 |

| 8 . . | . . . | . . 1 |

| 6 . . | . . . | . 3 . |

+-------+-------+-------+

| 3 . . | . . . | . . 5 |

| 2 . . | 9 . . | . . 6 |

| . 7 9 | . 6 5 | 8 1 . |

+-------+-------+-------+

All clues form a single connected chain, each adjacent to exactly two others, either diagonally or orthogonally.

This example has 90 degree rotational symmetry and the hole is therefore centered.

When creating a valid puzzle:

What is the largest hole that can be produced while maintaining at least some symmetry?

What is the largest hole that can be produced ignoring symmetry?

Can the size of the hole in a valid puzzle be increased by allowing clues to be adjacent to more than 2 cells?

Sudoku with 61 cell 'emtpy space'

- Code: Select all
`+-------+-------+-------+`

| . . 9 | 1 . . | . . . |

| . 8 7 | 2 . . | . . . |

| . . . | . . . | . 5 2 |

+-------+-------+-------+

| . . . | . . . | 1 2 9 |

| . . . | . . . | . . . |

| 4 5 6 | . . . | . . . |

+-------+-------+-------+

| 9 3 . | . . . | . . . |

| . . . | . . 5 | 3 4 . |

| . . . | . . 4 | 7 . . |

+-------+-------+-------+

An 'empty space' is an area of any shape that has no clues in it and does not surround any clues or group of clues completely.

This example has 180 degree rotational symmetry.

What is the largest empty space that can be made, with/without some symmetry?